Cryptography is one of the enabling technologies for today's digital society. Cryptography provides the tools used to achieve confidentiality and authenticity in networks which are a necessity for eCommerce and Government applications, private online communication and any form of secure outsourcing of data and computation. The conjectured advent of quantum computers challenges the security of many cryptographic systems. Indeed, many systems will get entirely broken. The development of secure and practical alternatives is probably the greatest and most urgent real-world challenge the cryptographic community is facing this century. Over the last few years large standardization bodies like NIST, IETF, and ETSI initiated projects to select and standardize post-quantum cryptographic systems. Due to the urgency of the issue and the time that standardization efforts and deployment take this was an important step. However, the post-quantum security of most proposed systems and protocols is still lacking a solid foundation: -Security proofs do not support the hardness of actual cryptographic schemes as they are non-tight. -It is unknown how to make existing applications of cryptography post-quantum secure without losing the existing security guarantees. This project will tackle these problems for the case of secure communication. Communication is probably the most urgent use-case of post-quantum cryptography as adversaries can store encrypted communication today and decrypt it when a quantum computer is built. The project has two work packages. The first work package covers tight provable security of basic primitives. The second work package covers their use to build communication protocols with tight security. The project will not only produce new tightly post-quantum secure building blocks and versions of TLS, WireGuard, and OTR. To make the results reusable, the project will provide a toolbox for tight security proofs in a post-quantum setting and generic transforms to turn existing communication protocols into tightly post-quantum-secure protocols.